Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Thermodynamics ↓


Entropy and free energy


In the field of thermodynamics, two important concepts emerge—entropy and free energy. These concepts are fundamental to understanding how chemical processes occur and how energy changes occur in a system. At first glance they may seem complex, but with clear explanations and examples, they can be easily understood. This detailed discussion aims to comprehensively cover these topics in a simple manner.

Understanding entropy

Entropy is a measure of the disorder or irregularity in a system. In thermodynamics, it describes how energy is distributed in a system and how that distribution affects the system's ability to do work. The concept of entropy is closely linked to the second law of thermodynamics, which states that the entropy of an isolated system always increases over time.

Let us consider a simple example—ice melting into water. Initially, the water molecules in ice are arranged in a structured, crystalline form with low disorder. As the ice melts, the structure breaks down, and the water molecules move around more freely, increasing the entropy of the system.

Mathematical expression of entropy

The mathematical expression for the change in entropy, ΔS, can be defined as:

ΔS = Q/T

where Q is the heat added to the system, and T is the absolute temperature. This equation states that the entropy change is directly proportional to the heat exchanged and inversely proportional to the temperature.

OrderDisorder

The diagram shows the progression from order to disorder, which symbolizes the concept of entropy in a system. As the system progresses from left to right, its entropy increases.

Understanding free energy

Free energy is an important concept in determining the spontaneity of a process. It combines enthalpy, entropy, and temperature to predict whether a reaction will occur without external intervention. The two main types of free energy are Gibbs free energy and Helmholtz free energy.

Gibbs free energy

Gibbs free energy (G) provides insight into reactions at constant pressure. The change in Gibbs free energy, ΔG, is given by:

ΔG = ΔH - TΔS

Where ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy. Negative value of ΔG indicates spontaneous process, while positive value indicates non-spontaneous.

Example of Gibbs free energy

Consider the process of water evaporating. At a given temperature, we can calculate the Gibbs free energy for the phase transition. If ΔG is negative, then water will spontaneously evaporate under those conditions.

Helmholtz free energy

The Helmholtz free energy (A) is used for systems with constant volume. It is expressed as:

ΔA = ΔU - TΔS

Here, ΔU is the change in internal energy. Although less common than ΔG in chemistry, the Helmholtz free energy can be important for some physics applications.

Relation between entropy and free energy

Entropy and free energy are interconnected through their collective role in determining the probability and direction of physical and chemical processes. A basic understanding is necessary to predict reaction outcomes and use energy efficiently.

As shown in the first equations, ΔG and ΔA integrate entropy to account for the dispersion and distribution of thermal energy within a system. This relation emphasizes that even if the energy of a system is reduced (enthalpicly favorable), disorder must also be considered to understand the full picture of the spontaneity of the process.

Example of entropy and free energy in a chemical reaction

Consider the combustion of methane:

CH₄ + 2O₂ → CO₂ + 2H₂O

In this exothermic reaction, heat is released (negative ΔH), and the entropy of the system increases (positive ΔS) because the products are in a more disordered gaseous state. The combined effect of energy release and increased disorder ensures that ΔG is negative, so the reaction is spontaneous.

ReactantsProducts

The illustration above shows the transformation from reactants to products in the combustion of methane. An increase in entropy and a decrease in Gibbs free energy drive the reaction forward.

Conclusion

Entropy and free energy serve as cornerstones in the field of thermodynamics within physical chemistry. Entropy provides an understanding of disorder and randomness, while free energy predicts the spontaneity of processes. Both concepts are essential in the study and application of chemical reactions and energy transformations. By decoding these principles, scientists and engineers can design processes that optimize energy use and sustainability.


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Entropy and free energy

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